modular apparatus for electrostatic actuation of common atomic force microscope cantilevers

Modular apparatus for electrostatic actuation of common atomic force microscope cantilevers , Christian J Long and Rachel J Cannara Citation: Rev Sci Instrum 86, 073703 (2015); doi: 10.1063/1.4926431 View online: http://dx.doi.org/10.1063/1.4926431 View Table of Contents: http://aip.scitation.org/toc/rsi/86/7 Published by the American Institute of Physics REVIEW OF SCIENTIFIC INSTRUMENTS 86, 073703 (2015) Modular apparatus for electrostatic actuation of common atomic force microscope cantilevers Christian J Long1,2,a) and Rachel J Cannara1 Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA Maryland Nanocenter, University of Maryland, College Park, Maryland 20742, USA (Received 30 December 2014; accepted 25 June 2015; published online 27 July 2015) Piezoelectric actuation of atomic force microscope (AFM) cantilevers often suffers from spurious mechanical resonances in the loop between the signal driving the cantilever and the actual tip motion These spurious resonances can reduce the accuracy of AFM measurements and in some cases completely obscure the cantilever response To address these limitations, we developed a specialized AFM cantilever holder for electrostatic actuation of AFM cantilevers The holder contains electrical contacts for the AFM cantilever chip, as well as an electrode (or electrodes) that may be precisely positioned with respect to the back of the cantilever By controlling the voltages on the AFM cantilever and the actuation electrode(s), an electrostatic force is applied directly to the cantilever, providing a near-ideal transfer function from drive signal to tip motion We demonstrate both static and dynamic actuations, achieved through the application of direct current and alternating current voltage schemes, respectively As an example application, we explore contact resonance atomic force microscopy, which is a technique for measuring the mechanical properties of surfaces on the sub-micron length scale Using multiple electrodes, we also show that the torsional resonances of the AFM cantilever may be excited electrostatically, opening the door for advanced dynamic lateral force measurements with improved accuracy and precision C 2015 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4926431] I INTRODUCTION A wide variety of actuation methods have been explored for the alternating current (AC) excitation and direct current (DC) displacement control of atomic force microscope (AFM) cantilevers Among these methods are piezoacoustic,1 magnetic,2,3 photothermal,4,5 and electrostatic excitation.6–9 Piezoacoustic excitation is by far the most frequently used technique In piezoacoustic excitation, a piezoelectric transducer is used to shake the AFM cantilever chip Unfortunately, this piezoelectric transducer also shakes other parts of the AFM, most notably the tip holder assembly, exciting the mechanical resonances of these other structures Due to the small quality factor of the spurious mechanical resonances compared to the AFM cantilever, their contribution to the motion of the cantilever tip can often be safely ignored; however, when the quality factor of the cantilever is sufficiently small (for example, in contact resonance measurements or measurements in an aqueous environment), the spurious mechanical resonances can completely obscure the mechanical resonance of the cantilever, leading to a so-called “forest of peaks” in the cantilever excitation spectrum.10 Even in cases where the cantilever resonance is not completely obscured, the resonance peak is often distorted, which can affect the accuracy of certain AFM techniques such as frequency modulation and phase modulation imaging.11–13 Further, the spurious resonances can a)Author to whom correspondence should be addressed Electronic mail: christian.long@nist.gov 0034-6748/2015/86(7)/073703/9 drift with time, leading to instabilities in imaging conditions and generally reducing the accuracy of AFM measurements.11 These problems can largely be overcome using electrostatic excitation In contrast to piezoacoustic actuation, electrostatic excitation only applies force to the AFM cantilever This localized excitation force removes the spurious mechanical resonances from the cantilever actuation transduction chain, providing a near-ideal transfer function from the cantilever drive signal to the cantilever displacement In order to take advantage of this fact, a variety of specialized cantilevers with integrated microelectrodes have been designed.8,14–16 Although this integrated device approach to electrostatic actuation works well, there has not been widespread adoption of these cantilevers This is likely due to the lack of variety in tip materials, cantilever geometries and spring constants, and the relatively high cost of probes with integrated microelectrodes in comparison to more common cantilever designs In addition to integrated microelectrodes, it has been shown that the optical fiber in an interferometry-based AFM may be metallized to allow for electrostatic excitation.6,17 However, this type of AFM is less common than optical-lever based AFMs, and this configuration requires that the positioning of the laser used for optical detection coincides with the location of the electrostatic excitation electrode In this work, we introduce a cantilever holder that has an independent, micropositionable electrode or electrodes near the back of the cantilever This module enables electrostatic excitation while maintaining compatibility with a wide variety of inexpensive, commercially available cantilevers 86, 073703-1 © Author(s) 2015 073703-2 C J Long and R J Cannara In Sec II, we describe the cantilever holder and the design of the actuator electrode In Secs III and IV, we discuss DC and AC biasing schemes for cantilever actuation, respectively For DC biasing, we show that the electric field from the actuator electrode is screened by the cantilever and does not affect the tip-sample interaction For AC biasing, we show that electrostatic excitation results in exceptionally clean cantilever actuation spectra In Sec V, we apply electrostatic excitation to demonstrate contact resonance spectroscopy and imaging, which are typically difficult to perform using piezoacoustic actuation In Sec VI we demonstrate torsional cantilever excitation by two electrostatic excitation electrodes located behind the cantilever Finally, in Secs VII and VIII, we discuss the results and conclude All measurements are performed in ambient air at room temperature II CANTILEVER HOLDER FOR ELECTROSTATIC ACTUATION The electrostatic actuation cantilever holder is shown in Fig The actuation electrode is a platinum/iridium wire that is held by friction within a stainless steel tube, making replacement of the electrode simple The stainless steel tube is mounted on a spring clip that has a positioning screw mounted on it This positioning screw enables the actuation electrode to be precisely positioned (±2 µm) with respect to the back of the cantilever In practice, we find that the ideal gap size between the cantilever and the actuation electrode is approximately 10 µm Making the cantilever-electrode gap larger reduces the Rev Sci Instrum 86, 073703 (2015) strength of the electrostatic force between the cantilever and the electrode, but making it smaller increases the damping of the cantilever due to squeeze-film damping in the gap between the cantilever and the actuation electrode The end of the platinum iridium wire that is near the cantilever is either tapered (as in Fig 1(b)) or angled (as in Fig 1(d)), permitting optical access to the end of the cantilever This access is critical for sensing cantilever deflection, which we accomplish using the typical optical beam-bounce and quadrant-photodiode detection scheme (Fig 2) The apex of the wire is polished to lie parallel to the cantilever plane In order to maximize electrostatic coupling to the fundamental flexural mode of the cantilever, the electrode surface should cover as much of the cantilever as possible while leaving sufficient surface area exposed to accommodate the laser spot For optimal excitation of cantilever eigenmodes above the fundamental, the electrode should be centered at a displacement antinode of the eigenmode of interest, ideally covering one half-wavelength of the eigenmode The position of the cantilever chip in its spring-clip mount sets the location of the electrode along the long axis of the cantilever In addition, the area of overlap between the cantilever and the electrode can be adjusted by moving the cantilever chip laterally along a tapered electrode, as shown in Fig 1(d) Electrical contact to the cantilever is made using a metal contact pad located on a printed circuit board (PCB), which is visible in Figs 1(a), 1(c), and 1(d) The cantilever springclip pushes the back of the cantilever chip against this contact pad, providing a large contact area Alternatively, the metal FIG (a) shows a photograph of the tip holder detailing how the actuation electrode is mounted (b) shows a close-up view of a straight actuation electrode in proximity to the cantilever, demonstrating the ability to accommodate the optical path of the laser beam (c) A tilted view shows the L-shape of the electrode in this version of the module, corresponding to the holder shown in (a); the electrical connections to the cantilever and actuation electrode are schematized in blue and red, respectively In (d), a further close-up view of the actuation electrode and cantilever shows the tapered shape of the electrode, which allows the user to adjust the overlap area between the electrode and the cantilever 073703-3 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015) acquired As the electrode nears the back of the cantilever, the strength of the actuation increases and the quality factor of the cantilever decreases due to squeeze-film damping of the air in between the electrode and the cantilever The decrease in the quality factor for a 10 µm electrode-cantilever gap depends on the particular electrode and cantilever, but it is comparable to that caused by the tip-sample interaction, as commercial cantilevers often have a tip that is approximately 10 µm long III DC DISPLACEMENT CONTROL IN COMMON AND DIFFERENTIAL MODES FIG Schematic of electrical connections to the sample, cantilever, and actuator electrode Vc is a common bias to both the cantilever and electrode, while Vd is a differential bias between the actuation electrode and the cantilever The connection of the sample to ground is optional, though it is useful for conducting samples in order to establish a well-defined surface potential spring clip holding the cantilever chip can be used to make electrical contact to the cantilever, though the contact area to the cantilever chip is smaller in this case We typically use cantilevers that have a metal backside (beam-bounce detector side) coating that is contiguous between the cantilever and the cantilever chip for connectivity between the PCB contacts and cantilever However, we have had equal success with doped Si cantilevers that have no metal coating We find that the most challenging aspect of using the electrostatic actuation module presented here is loading the cantilever chip and aligning the actuation electrode with the back of the cantilever With some practice, however, this procedure has become routine and, in terms of cantilever loss, as reliable as standard cantilever mounting procedures The alignment is typically performed under a binocular microscope with a working distance of approximately 10 cm and a magnification ranging from 6.7× to 50× Low magnification is used to align the electrode in the plane of the cantilever, and high magnification is used to set the gap between the electrode and the cantilever To align the cantilever to the actuator electrode, the electrode is first raised far enough above the mounting plane of the cantilever chip to avoid risk of breaking the cantilever The cantilever chip is then inserted under the cantilever spring-clip, and the tip holder is placed under a microscope (6.7× magnification) in plan view (tip apex pointing towards the microscope objective) Next, the electrode is aligned with the long axis of the cantilever by adjusting the cantilever chip position with tweezers The tip holder is then rotated to view the gap between the electrode and the cantilever (at 50× magnification), and the electrode is approached to the cantilever using the electrode positioning screw until there is a gap of approximately 10 µm Alternatively, a larger gap may be left in between the cantilever and the electrode followed by a fine approach with the tip holder mounted inside the AFM In this case, once the cantilever holder is mounted inside the AFM, the electrode positioning screw is used to approach the electrode to the cantilever back while actuation spectra are continuously For the electrode configurations shown in Figs and 2, there are two DC-voltage biasing schemes that can be applied In the first scheme, which we will call common mode, one applies a common bias voltage to both the actuation electrode and the cantilever (Vc in Fig 2) In practice, the bias in common mode is applied relative to a ground plane that may be the surface of a conducting sample, an electrode located below an insulating sample, or a conductor located far from the tip (e.g., the AFM chassis) In the second mode, which we will call differential mode, one applies a potential difference between the actuation electrode and the cantilever (Vd in Fig 2) For comparison with these modes, we also discuss a simple tip-bias experiment where a DC voltage is applied to a cantilever without an actuation electrode, as might be typical in piezoresponse force microscopy (PFM),18 electrostatic force microscopy (EFM),19 or kelvin probe force microscopy (KPFM).20 In this case, it is well known that the force on the tip (Ft s ) depends on the tip-sample capacitance 21 ts (Ct s ) gradient and may be modeled as Ft s = 21 ∂C ∂z Vt s ; here, z is the tip displacement (with the z-axis directed along the normal to the back of the cantilever), Vt s is the potential difference between the tip and the sample, and we have taken Vt s to include any applied tip bias and the contact potential difference between the tip and sample Qualitatively, the tipsample electrostatic force in this case is attractive, increases as the tip nears a sample surface, and scales quadratically with applied bias This tip-sample distance-dependence and quadratic forcedependence may be seen in Fig 3(a), where we swept the DC bias applied to a cantilever and measured the cantilever deflection for several tip-sample gap sizes The bias on the cantilever was applied with respect to a grounded conducting sample—here a piece of highly oriented pyrolytic graphite (HOPG) When the tip-apex was far from the sample (approximately cm tip-sample gap, blue curve in Fig 3(a)), the tipsample electrostatic force was relatively weak compared to when the tip-apex was near the sample (approximately µm tip-sample gap, black curve in Fig 3(a)) We note that the offset of the parabolas from zero bias was caused by a combination of analog offsets in the bias electronics and the contact potential difference between the tip and sample materials Applying a common mode bias using the electrostatic actuator (Fig 3(b), blue, red, and black curves) results in a very similar force-distance and force-voltage behaviors as compared to a simple tip-bias without the electrostatic actuation electrode (Fig 3(a)) The primary difference is that the force on the cantilever is somewhat larger for common mode 073703-4 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015) FIG Bias voltage and tip-sample distance dependence of electrostatic forces (a) shows bias parabolas for a cantilever (without an actuation electrode behind it) above a grounded HOPG sample (b) shows bias parabolas for differential mode (dotted lines, labeled DM) and common mode (solid lines, labeled CM) biasing schemes taken at different heights above a grounded HOPG sample (c) shows bias parabolas with the same configuration as (b), except using a cleaved mica sample in place of HOPG (d) shows the approach part of force curves taken with the bias voltages marked with circles in (b) The same cantilever was used for (a) through (d); the cantilever was a model PPP-CONTR (Nanosensors, Neuchatel Switzerland)36 that had a spring constant of approximately 0.27 N/m All bias parabolas were acquired using a triangular bias ramp with a period of Hz The precision of the cantilever deflection given by a single standard deviation was less than the width of the plot lines The cantilever deflection was calibrated using the contact part of an approach curve, which we estimate results a relative accuracy of better than ±10% than for a simple tip-bias This is most readily visible by comparing the bias parabolas for these modes when the tipapex is µm from the surface (solid black curves in Figs 3(a) and 3(b)) Between these two curves, the bias parabola for common mode shows a moderately larger deflection per voltage squared than the simple tip-bias We attribute this increase in force to the addition of the electrode behind the cantilever Physically, since the electrode is held at the same potential as the cantilever in common mode operation, the charge on the cantilever and the electrode will have the same sign, resulting in a repulsive interaction between them and increasing the force on the cantilever in the direction of the sample The increase in force available in common mode over a simple tip-bias may be useful for applications such as 3D lithography, where electrostatic forces between a cantilever and a substrate have been used to control cantilever position with exquisite precision.22 The primary drawbacks to using common mode biasing for DC displacement control are that the actuation force depends strongly on the tip-sample distance and that the sample is immersed in the electric field from the cantilever and tip Indeed, we find that the electric field from the tip can be a problem for electrostatic actuation on insulating samples, where surface charge redistribution can change the sample’s surface potential Such a case is illustrated in Fig 3(c), where charge redistribution on the surface of a mica sample results in hysteresis of the tip-sample electrostatic force when increasing and decreasing the common mode bias In contrast, these drawbacks are largely resolved by using differential mode In differential mode, the gap between the electrode and the cantilever does not depend on the tip-sample distance, eliminating the variation in actuation force with tip-sample distance Figure 3(b) shows a comparison of bias parabolas for common mode and differential mode that were measured with different tip-sample gaps with the common mode bias set to V The most obvious difference between these modes is that for differential mode, the cantilever is pulled away from the sample surface (towards the actuation electrode), while for common mode, the cantilever is pulled towards the sample surface More importantly, for differential mode, there is very little variation in the bias parabolas at different tip-sample gap sizes (dotted curves with purple, green and cyan coloring in Figs 3(b) and 3(c)), while for common mode (solid curves with blue, red, and black coloring in Figs 3(b) and 3(c)) and simple tip biasing (solid curves with blue, red, and black coloring in Fig 3(a)), there is a strong dependence on the tip-sample gap size This behavior is consistent with our expectation that 073703-5 C J Long and R J Cannara Rev Sci Instrum 86, 073703 (2015) for differential mode, the electric fields are largely contained in the gap between the actuation electrode and the cantilever, while for common mode, the electric fields are located below the tip and therefore show a strong dependence on the tipsample distance This also provides some evidence that in differential mode, the stray electric field from the actuation electrode does not affect tip-sample forces In order to verify that the stray electric fields in differential mode not interfere with the tip-sample interaction even when the tip is very near the sample, we took force curves using both common mode and differential mode biasing schemes, as shown in Fig 3(d) For these force curves, the applied differential mode bias was set to zero when taking force curves in common mode, and vice versa For both modes, the out-of-contact deflection of the cantilever shifts with applied bias, which is consistent with the bias dependence shown in Fig 3(b) Again as expected, the cantilever was displaced away from the sample for differential mode, while for common mode, the displacement was towards the sample The most interesting behavior occurs as the tip nears the surface: in common mode operation, the long-range electrostatic force between the tipapex and the sample causes the cantilever to bend towards the surface just before snap-in (red and black curves in Fig 3(d)); however, for differential mode, the deflection is completely flat until the snap-in point These observations imply that for differential mode, the bias on the actuation electrode is screened by the (grounded) cantilever and therefore does not interfere with the tip-sample interaction This screening effect is consistent with the behavior of AFM probes containing an integrated electrostatic shield.23 By combining both the common mode and differential mode biasing schemes, the net electrostatic force on the cantilever can be either positive or negative, essentially doubling the range of cantilever positions that can be obtained when compared to traditional tip-sample based electrostatic actuation Alternatively, the electrostatic interaction between the tip and sample can be nulled using a common mode bias (as in KPFM), while the position of the cantilever can still be controlled by applying a differential mode bias IV DYNAMIC EXCITATION In order to excite the cantilever for dynamic AFM modes, we introduce a biasing scheme that has an AC component in addition to a DC component To avoid electrostatic tip-sample interactions, we consider operation in differential mode (Vc = 0) and apply a differential bias that contains both an AC and a DC component, Vd = VDC + VAC sin(ωt), (1) where VDC includes the work function difference between the cantilever and the actuation electrode as well as an externally applied voltage In order to estimate the force on the cantilever in differential mode, we approximate the cantilever-electrode gap as a parallel plate capacitor with capacitance Cd and ∂C take the force (Fd ) on the cantilever to be Fd = 12 ∂zd Vd The resulting force on the cantilever can be written as F = FDC + Fω + F2ω , where ( ) ∂Cd 2 FDC = VDC + VAC , ∂z ∂Cd Fω = VDC VAC sin (ωt) , ∂z (2) (3) and F2ω = − ∂Cd V cos (2ωt) ∂z AC (4) The DC component of the force adds an offset to the equilibrium position of the cantilever and is trivially ignored in experimental operation This leaves two frequency components, one at angular frequency ω and another at angular frequency 2ω For single frequency operation, one would ideally apply a DC bias such that VDC = 0, thus nulling the actuation force at angular frequency ω One could then measure the cantilever response at 2ω However, exactly nulling the analog offsets in the bias electronics and accounting for the surface potential difference between the actuator electrode and the cantilever can entail significant effort In practice, we have found that it is often sufficient to apply a DC bias between the cantilever and the actuation electrode such that VDC ≥ VAC and then match the AC drive frequency to the resonance frequency of the cantilever In this case, since Fω is at the resonance frequency of the cantilever and F2ω is above the resonance, the cantilever response is primarily at angular frequency ω, with negligible actuation at the second harmonic The degree to which VDC should exceed VAC depends on the quality factor of the cantilever resonance, where low quality factor resonances require a larger ratio of VDC to VAC in order to effectively suppress the cantilever excitation at the second harmonic A comparison of cantilever actuation spectra using electrostatic and piezoacoustic actuation appears in Fig Figure 4(a) shows an example cantilever actuation spectrum taken using our electrostatic actuator The electrostatic actuation spectrum is ideal in the sense that it only shows the resonances corresponding to the first two flexural modes of the cantilever The accuracy of the actuation is highlighted by the excellent agreement between the measured actuation spectrum (red) and a curve fit to a damped harmonic oscillator model for the fundamental eigenmode of the cantilever (black) Figure 4(b) shows an example actuation spectrum taken using the common “tip shaker” (a standard cantilever holder on a Cypher AFM, Asylum Research/Oxford Instruments, Santa Barbara, CA) as well as a curve fit to a damped harmonic oscillator model for the fundamental eigenmode The piezoacoustic actuation spectrum exhibits multiple spurious resonances with amplitudes comparable to the flexural modes of the cantilever, resulting in poor agreement between the measured actuation spectrum and a damped harmonic oscillator model Figure 4(c) shows the thermal motion of the cantilever in the absence of an external actuator The thermal spectrum exhibits peaks at the same frequencies as the electrostatically actuated spectrum, clearly identifying these resonances as the flexural modes of the cantilever We note that the vertical axes are in voltage (mV) rather √ than distance (nm) for Figs 4(a) and 4(b) and in V/ Hz for Fig 4(c) because the optical lever sensitivity differs for 073703-6 C J Long and R J Cannara FIG Measured cantilever actuation spectra for several different actuation mechanisms, with the first two flexural modes of the cantilever highlighted in gray (a) A frequency spectrum showing the cantilever’s response to the electrostatic drive (red), the level of detector noise with the actuator turned off (blue), and a fit of an ideal damped harmonic oscillator to the cantilever response (black) (b) A frequency spectrum showing the cantilever’s response to a commercial piezoelectric actuator located behind the cantilever chip (red), the level of detector noise with the actuator turned off (blue), and a damped harmonic oscillator fit (black) (c) Power spectral density (PSD) spectrum showing thermal motion of the cantilever at ambient temperature (red) and detector noise with the laser spot on a rigid surface (blue) The electrostatic drive in (a) does not exhibit the spurious resonances that are apparent when using tip piezo-drive in (b) The cantilever used here was a model DCP-11 (NT-MDT, Moscow, Russia) that had a spring constant of approximately 11 N/m the first and second flexural modes of the cantilever For the fundamental mode (at ≈151 kHz), the optical lever sensitivity was approximately 40 nm/V For piezoacoustic actuation, the amplitude of the drive voltage was 100 mV; for electrostatic actuation, the drive amplitude was V with an additional DC bias of V between the actuator electrode and the cantilever Although the drive voltage was higher for electrostatic actuation than for piezoacoustic actuation, it was still well within the ±10 V range that is typical for auxiliary voltage sources on AFM instruments The dynamic electrostatic actuation response demonstrated here enables exceptionally clean cantilever excitation that does not depend on the electrical properties of the sample or require a specialized cantilever V CONTACT RESONANCE MICROSCOPY Contact resonance spectroscopy and imaging are mechanical property characterization techniques that can nondestructively probe the elastic storage moduli and viscoelastic loss moduli of materials on the nanometer length scale.24,25 For contact resonance spectroscopy, the elastic properties of the sample are probed by measuring the resonance frequency and quality factor of a cantilever while it is free and then measuring them again while it is in contact with a sample of interest.26 For contact resonance imaging, the contact resonance frequency is tracked in real time while the tip is scanned over a sample surface in contact mode.27,28 In general, by applying suitable models for the cantilever beam dynamics and the tip-sample contact mechanics, one can use the measured free and contact resonance frequencies to obtain quantitative values for the elastic modulus of Rev Sci Instrum 86, 073703 (2015) a sample A variety of different modeling approaches have been used for this purpose and have been applied with a great deal of success to both hard materials and to soft materials that exhibit viscoelastic behavior.23,29 In this work, we confine ourselves to demonstrating the utility of electrostatic actuation for measuring contact resonance frequencies, without emphasizing any particular modeling approach for extracting quantitative mechanical property information from the contact resonance observables For contact resonance measurements, the cantilever resonance is often strongly damped when the tip is brought into contact with the sample, making the quality factor of the relevant eigenmodes comparable to or even smaller than the quality factors of the spurious mechanical resonances of the AFM In order to avoid exciting these spurious resonances, contact resonance measurements are often performed using a piezoelectric sample actuator instead of piezoacoustic actuation of the tip.23 Sample actuators for contact resonance tend to be mechanically simpler than a tip shaker, as well as more mechanically damped Thus, the use of sample actuators reduces the probability of exciting spurious mechanical resonances in the AFM but does not eliminate them Sample actuators also typically require that the sample be glued to (and later removed from) the actuator surface to minimize unwanted mechanical resonances Thus, compared to piezoelectric actuation of the tip or sample, electrostatic actuation provides several advantages: it provides direct cantilever excitation to eliminate spurious mechanical resonances, it does not require any special sample preparation, and it is compatible with smallsample AFMs, where adding a bulky sample actuator can be challenging In order to demonstrate contact resonance spectroscopy and imaging by electrostatic actuation, we explored a sample consisting of patterned titanium squares on a silicon substrate Contact resonance spectra and images of this sample are shown in Fig Figure 5(c) shows contact resonance spectra for the free cantilever (black), the cantilever in contact with the titanium (red), and the cantilever in contact with the silicon (blue) Since the electrostatic actuator only excites the resonance of the cantilever, the resonance peaks are straightforward to identify and have the expected damped harmonic oscillator shape The clean transfer function from excitation signal to force on the cantilever also greatly simplifies contact resonance imaging, because there are no spurious resonance peaks for the frequency feedback loop to mistakenly follow, even when it deviates significantly from the true resonance frequency Figure 5(b) shows a contact resonance image obtained on the titanium-on-silicon sample using dual-amplitude resonance tracking,24 which is a technique for tracking the resonance frequency of the cantilever as the tip is scanned in contact with a sample surface The observed contact resonance frequency for titanium is lower than for silicon, which is consistent with the fact that titanium is the more compliant material VI TORSIONAL EXCITATION Next, we demonstrate torsional excitation of the cantilever using electrostatic forces Torsional excitation has applications 073703-7 C J Long and R J Cannara FIG Contact resonance images of patterned titanium metal on a silicon substrate (a) shows the topography of the sample, which consists of approximately 280 nm thick titanium islands (b) shows the contact resonance frequency as the tip is scanned across the surface (c) shows contact resonance spectra for the free cantilever (tip located approximately 100 nm above the sample surface) and for the cantilever in contact with the titanium and silicon surfaces at a normal load of (300 ± 30) nN Peaks labeled Mode correspond to the fundamental flexural mode of the cantilever, while Mode refers to the first flexural overtone The main source of uncertainty in the cantilever amplitude in (c) was given by the detector noise, which contributed a root mean square amplitude noise of less than 0.2 (arbitrary unit) at all measurement frequencies The cantilever was a model PPP-NCLR (Nanosensors, Neuchatel Switzerland) that had a spring constant of (25.3 ± 2.5) N/m The spring constant was calibrated using the thermal spectrum method.37 The uncertainties in the spring constant correspond to ±10% relative error, which is considered to be a conservative estimate of the relative accuracy of this technique.38 in tribology, nanomechanical characterization, and force spectroscopy In the past, excitation of torsional cantilever modes has most frequently been performed with a split piezoelectric actuator, which shakes the cantilever chip in a rocking motion.30,31 Torsional excitation has also been performed using a shear-wave piezoelectric sample transducer32 and using the (non-split) piezoacoustic tip actuator that is typically present in most AFMs.33 Unfortunately, piezoacoustic actuation of the torsional mode is susceptible to the same “forest of peaks” as piezoacoustic excitation of the flexural cantilever modes, again making electrostatic actuation an attractive alternative Here, the torsional modes of a cantilever are excited using two electrodes that are offset laterally with respect to the long axis of the cantilever A schematic of this configuration is shown in Fig 6(b), and an image of a dual-electrode actuator is shown in Fig 6(c) In torsional excitation mode, the two electrodes carry a common DC bias, while the AC bias is driven 180◦ out-of-phase between the two electrodes This biasing scheme causes one electrode to increase the force on one side of the cantilever while the force due to the other electrode decreases, causing the cantilever to undergo a torque The two electrodes may also be used to perform flexural excitation by driving the AC bias on both electrodes in-phase, as shown in Fig 6(a) Figure 6(d) shows cantilever actuation spectra obtained using this dual-electrode actuator for both the torsional Rev Sci Instrum 86, 073703 (2015) FIG Excitation of flexural and torsional cantilever modes using multiple electrodes (a) shows a schematic in which both actuation electrodes are driven in-phase to excite the flexural modes of the cantilever In (b), the actuation electrodes are driven with a common DC bias but with an out-ofphase AC bias to excite torsional modes of the cantilever (c) shows an optical microscope image of a dual-electrode electrostatic actuator with a cantilever aligned to the electrodes (d) The flexural and torsional actuation spectra are shown for the setup in (c) The cantilever is a model RC800PSA (Olympus, Tokyo, Japan) For both flexural and torsional excitations, a DC bias of V and an AC bias of V were applied to the electrodes and flexural excitation schemes Of course, it is also possible to excite both a flexural resonance and a torsional resonance simultaneously In this case, the electrodes are driven in-phase at the fundamental flexural mode frequency (ω f ) and have an additional out-of-phase component at the torsional resonant frequency (ω t ) We note that for the dual-electrode configuration, it is difficult to perfectly align the centerline between the electrodes to the long axis of the cantilever This imperfect alignment causes some cross talk between the torsional and flexural excitation schemes outlined above This cross talk appears in Fig 6(d) as small peaks in the flexural excitation spectrum, which correspond to torsional resonances, and vice versa To avoid this cross talk, we have found that it is possible to measure the excitation spectrum for each electrode independently and then adjust the drive voltage on each electrode to obtain equal forces VII DISCUSSION In addition to providing a clean transfer function, electrostatic actuation has applications that cannot be achieved using piezoelectric actuators These expanded applications arise from the location of the driving force on the cantilever For piezoacoustic excitation, the force is applied at the base of the cantilever, while for electrostatic actuation, the force is applied at or near the end of the cantilever, without relying on a sample actuator that functions solely in contact (or very near contact) with a surface Applying forces at the end of the cantilever allows one to dynamically balance the tip-sample force during approach, effectively eliminating snap-in and snap-off instabilities.34 Applying forces at the end of the cantilever also enables more 073703-8 C J Long and R J Cannara accurate measurement of the tip displacement because one does not need to account for the displacement of the base of the cantilever, as in piezoacoustic excitation This is particularly important when shaking the cantilever well below or above its resonance frequency, where the motion of the cantilever base induced by piezoacoustic excitation can be comparable to or larger than the motion of the tip Electrostatic actuation of AFM cantilevers, as described here, may be used to image any type of material, including both conducting and insulating samples, and is compatible with a wide variety of cantilever materials However, there are some considerations to be made when choosing a cantilever For example, the electrode can obscure the beam-bounce optical path when placed directly above a relatively small cantilever To minimize this effect, we find it simplest to use cantilevers that are longer than 100 µm However, for cantilevers smaller than this, it may be possible to use a transparent actuator electrode or an electrode that is located above the plane of the cantilever but offset slightly from the space directly above the cantilever In addition to long cantilevers, we prefer cantilevers for which electrical contacts are easily made, as is the case for doped silicon cantilevers or cantilevers with a metal coating on either the tip-side or the backside Ideally, this metal coating should be contiguous between a cantilever and its chip This demand for electrical contact to the cantilever may preclude the use of some cantilevers For example, performing electrostatic actuation on silicon nitride cantilevers with no metal backside coating could be challenging However, in this case, actuation may still be possible through dielectrophoretic forces or by embedding charge in the cantilever body before loading it into the tip holder Finally, although the current design of our electrostatic actuator is optimized for actuation in air, it has recently been demonstrated that electrostatic actuation may be performed in aqueous environments through the application of an amplitude-modulated high-frequency bias voltage.35 When combined with an actuation electrode behind the cantilever, such a biasing scheme removes yet another limit on electrostatic actuation, enabling it to be utilized in vacuum, air, or aqueous environments, with any sample and with a broad variety of commercially available cantilevers VIII CONCLUSION The electrostatic actuation module presented here provides an exceptionally clean mechanism for actuating many types of common AFM cantilevers, making it possible to bring the accuracy of electrostatic actuation to bear on wide variety of cantilever geometries and tip materials Our approach is compatible with both conducting and insulating samples, is relatively inexpensive, and may be adapted to retrofit existing AFM systems We have shown that electrostatic actuation is particularly useful in contact resonance measurements, where tip-sample damping may lead to reduced quality factors, thereby diminishing the ability to distinguish cantilever resonances from spurious ones Using multiple electrodes, we have also shown that it is possible to excite the torsional modes of a common AFM cantilever directly, opening the door for improved dynamic lateral force measurements Rev Sci Instrum 86, 073703 (2015) ACKNOWLEDGMENTS The authors are grateful to Fred 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noncontact calibration of colloidal probe sensitivities in atomic force microscopy,” Rev Sci Instrum 80, 065107 (2009)  ...REVIEW OF SCIENTIFIC INSTRUMENTS 86, 073703 (2015) Modular apparatus for electrostatic actuation of common atomic force microscope cantilevers Christian J Long1,2,a) and Rachel J Cannara1 Center for. .. from the location of the driving force on the cantilever For piezoacoustic excitation, the force is applied at the base of the cantilever, while for electrostatic actuation, the force is applied... Park, “Tapping mode atomic force microscopy using electrostatic force modulation,” Appl Phys Lett 69, 2831 (1996) 7N Kato, I Suzuki, H Kikuta, and K Iwata, ? ?Force- balancing microforce sensor with